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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Self Evaluation Test - Complex Numbers and Quadratic Equations

  • question_answer
    If the roots of the quadratic equation\[{{x}^{2}}+px+q=0\] are \[\tan 30{}^\circ \] and \[\tan 15{}^\circ \] respectively, then the value of \[2+q-p\] is

    A) 2  

    B) 3    

    C) 0                     

    D) 1

    Correct Answer: B

    Solution :

    Given equation is \[{{x}^{2}}+px+q=0\] Sum of roots \[=\tan 30{}^\circ +\tan 15{}^\circ =-p\] Product of roots \[=\tan 30{}^\circ .\tan 15{}^\circ =q\] \[\tan 45{}^\circ =\frac{\tan 30{}^\circ +\tan 15{}^\circ }{1-\tan 30{}^\circ .\tan 15{}^\circ }=\frac{-p}{1-q}=1\] \[\Rightarrow \,\,\,-p=1-q\,\,\,\,\Rightarrow \,\,\,q-p=1\] \[\therefore \,\,\,2+q-p=3\]


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